System And Method For Planning Support Removal In Hybrid Manufacturing With The Aid Of A Digital Computer

ABSTRACT

Algorithmic reasoning about a cutting tool assembly&#39;s space of feasible configurations can be effectively harnessed to construct a sequence of motions that guarantees a collision-free path for the tool assembly to remove each support structure in the sequence. A greedy algorithm models the motion of the cutting tool assembly through the free-spaces around the intermediate shapes of the part as the free-spaces iteratively reduce in size to the near-net shape to determine feasible points of contact for the cutting tool assembly. Each support beam is evaluated for a contact feature along the boundary of the near-net shape that constitutes a feasible point of contact. If a support beam has at least one feasible configuration at each point, the support beam is deemed ‘accessible’ and a collection of tool assembly configurations that are guaranteed to be non-colliding but which can access all points of contact of each accessible support beam can be generated.

FIELD

This application relates, in general, to hybrid manufacturing processesand, in particular, to a system and method for planning support removalin hybrid manufacturing with the aid of a digital computer.

BACKGROUND

Historically, the manufacturing of parts from raw stock or material hasinvolved two distinct, albeit combinable, manufacturing processes.Fabricating a part through subtractive manufacturing (SM) involvesprogressively removing or machining material from raw stock until thepart has been reduced to a rough form within a specified tolerance. InSM processes, raw material is often removed by turning, drilling, ormilling the part being fabricated. Drilling involves traversing arotating bit along a longitudinal axis while milling operates inthree-dimensional space. Following completion of SM processes,post-processing may be required to smooth, polish, finish, or otherwisetransform the part into final completed form.

Fabricating a part through additive manufacturing (AM) involvesprogressively adding or depositing material onto a part beingfabricated, often by adding successive layers, until the partapproximates an intended shape and size. However, in contrast to SM,many AM processes add support materials or scaffolding to the part beingfabricated as part of the AM process plan, so that the part does notcollapse under its own weight because the part being fabricated willcontinually increase in size and weight as manufacturing progresses.

While SM processes often end when a rough form of the desired part hasbeen achieved, AM processes may instead create a shape that stillrequires further transformation due to the addition of the scaffolding.This interim result is known as a near-net shape, which is the partbeing fabricated, plus any supports that were added during AMmanufacturing. Ordinarily, the near-net shape is post-processed toremove the scaffolding using a range of potential processes frommanually removing the supports with a chisel-like cutting tool toprogramming collision-free tool paths for a CNC-mill to remove thesupports, after which even further post-processing may be required totransform the part without scaffolding into final form.

Due to the need to remove scaffolding, AM can be characterized as one ofseveral manufacturing processes that may be needed to fabricate a part,rather than as a stand-alone solution, although removing scaffolding isbut one example of a manufacturing process that involves both AM and SMoperations. More generally, any sequence of AM and SM processes,independent of the ordering of their respective contributions, can bedefined as a hybrid manufacturing process. An approach to processplanning for hybrid manufacturing is described in U.S. Patentapplication, entitled “System and Method for Constructing Process Plansfor Hybrid Manufacturing with the Aid of a Digital Computer,” Ser. No.______, filed on even date herewith, pending, the disclosure of which isincorporated by reference.

In a hybrid manufacturing process, understanding the interactionsbetween

SM and AM operations is critical, especially when planning the layoutand removal of the supporting material generated by the AM process. Theinteraction of SM and AM processes creates a spatial planning problemthat requires the analysis of the feasible, that is, non-colliding,spatial configurations of tools to be used against a dynamic near-netshape that must be continually updated whenever a support is removed.The analysis also requires determining whether supports are being placedin locations during AM that will later be inaccessible to the cuttingtools used in the SM process.

Hybrid machines equipped with both AM and SM capabilities have emerged,including the Ambit™-Dextrous Manufacturing system, sold by HybridManufacturing Technologies, McKinney, Tex., and the Lasertec 65 3D, soldby DMG Mori Seiki Co., Nakamura-ku, Nagoya, Japan. These machinestypically couple a LENS (Laser Engineered Net Shaping) or similar directenergy deposition AM process with a high-axis milling center to enableAM parts fabrication on curved surfaces. However, LENS-type AM processesare not well suited to creating near-net shapes, which limits the rangeof parts that can be built.

Therefore, a need exists for an approach to planning removal ofAM-process-generated supports from a dynamic near-net shape through anSM process.

SUMMARY

Algorithmic reasoning about a cutting tool assembly's space of feasibleconfigurations can be effectively harnessed by an SM tool path plannerto construct a sequence of motions that guarantees a collision-free pathfor the tool assembly to remove each support structure in the sequence.A greedy algorithm models the motion of the cutting tool assemblythrough the free-spaces around the intermediate shapes of the part asthe free-spaces iteratively reduce in size to the near-net shape todetermine feasible regions (or points) of contact for the cutting toolassembly.

Each support beam is evaluated for a contact feature along the boundaryof the near-net shape that constitutes a feasible region of contact forthe tool assembly to either partially or totally remove the individualsupport beam. If non-existent, the part is found to benon-manufacturable because no SM process plan to cut the support beamsfrom the near-net shape, such that the part can be dislodged, exists.However, if a support beam has at least one feasible configuration ateach region of contact with the part, the support beam is deemed‘accessible’ and a collection of tool assembly configurations that areguaranteed to be non-colliding but which can access all regions ofcontact of each accessible support beam can be generated. Support beamsdeemed accessible in one iteration of the algorithm are removed from thenext iteration, so that the near-net shape gradually shrinks to thepart's shape.

An embodiment provides a system and method for planning support removalin hybrid manufacturing with the aid of a digital computer. A computeris provided with parameters for a machining tool assembly. Eachparameter includes orientations and positions of the machining toolassembly. The computer is also provided with a model of a part definingsurfaces and the interior of the part and one or more support structuresthat were added to the part during additive manufacturing. A near-netshape is modeled with the computer initially as the part combined withthe support structures. A configuration space is set up with thecomputer including geometric transformations that represent the spatialmotions of the machining tool assembly based upon the machining toolassembly's parameters. A manner of construction of each of the supportstructures is determined with the computer to provide contact featuresat an intersection of the support structures and the part. Each of thesupport structures is evaluated with the computer for the existence of acontact feature within free-space that is available within theconfiguration space around the near-net shape that includes a feasibleregion of contact for the tool assembly to remove all of the supportstructures that are accessible from the near-net shape. A collision-freesupport removal sequence is guaranteed to exist for every supportstructure in the set of accessible support structures. in furtherembodiments, various heuristics can be used to order the sequence ofsupport removals, for instance, minimizing orientation changes,minimizing time or cost, maximizing surface quality, and so forth.

While planning the support removal sequence, each newly removed supportstructure is added to a list representing the removal sequence and thenear-net shape is continually updated as each support structure isincrementally removed. For each of the support structures in the supportremoval sequence, a set of collision-free contact configurations of themachining tool assembly at the boundary feature is constructed with thecomputer, provided that boundary features are found for all of thesupport structures. Note that as each support is removed, the tool'sfeasible configuration space increases and increases the available spaceof motions for the next accessible support. Process plans includingmachining operations by the machining tool assembly are created with thecomputer based upon the sets of collision-free contact configurations ofthe machining tool assembly for the support structures. The machiningtool assembly is programmed with the computer with the process plans andthe machining tool assembly is operated per the machining operations inthe process plans by machining off the support structures.

Still other embodiments of the present invention will become readilyapparent to those skilled in the art from the following detaileddescription, wherein is described embodiments of the invention by way ofillustrating the best mode contemplated for carrying out the invention.As will be realized, the invention is capable of other and differentembodiments and its several details are capable of modifications invarious obvious respects, all without departing from the spirit and thescope of the present invention. Accordingly, the drawings and detaileddescription are to be regarded as illustrative in nature and not asrestrictive.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a side view showing, by way of example, a near-net shape asfabricated through AM processes.

FIG. 2 is a functional block diagram showing a system for planningsupport removal in hybrid manufacturing with the aid of a digitalcomputer in accordance with one embodiment.

FIG. 3 is a flow diagram showing a method for planning support removalin hybrid manufacturing with the aid of a digital computer in accordancewith one embodiment.

FIG. 4 is a flow diagram showing a routine for performing a greedyalgorithm to plan the removal of the support beams from the near-netshape for use in the method of FIG. 3.

FIG. 5 is a flow diagram showing a recursive routine for evaluatingmanufacturability of a part being fabricated for use in the routine ofFIG. 4.

DETAILED DESCRIPTION

Planning SM processes for removing scaffolding from an AM-producednear-net shape requires analysis of feasible non-colliding cutting toolconfigurations in a dynamically-changing space. As each support isremoved from the near-net shape, the space available to the cutting toolfor collision-free motion around the near-net shape changes, usually byincreasing the amount of free space within which a cutting tool assemblycan move. For each type of cutting tool to be used, a tool'sconfiguration includes a position and orientation. Thus, the combinationof the part and scaffolding, which constitute the near-net shape, andtool assembly configuration geometries together creates a complexproblem space for determining support removability through SM processes.

A support removal process plan for SM processes includes sequences ofsupport beams to be removed. FIG. 1 is a side view showing, by way ofexample, a near-net shape 10 as fabricated through AM processes. Supportstructures or scaffolding, often in the form of support beams 12, havebeen added during AM to support the part being fabricated 11. Thescaffolding is often organized in tree-like shapes to save material,which is eventually discarded or potentially reused for other purposes.For convenience, “support structure,” “scaffolding,” and “support beam”will be used interchangeably to refer to the support material that hasbeen added to a part being fabricated by AM processes. For each supportremoval sequence generated, a tool path planner, such as acomputer-aided manufacturing (CAM) system, or a system using motionplanning algorithms, for instance, the Open Motion Planning Library(OMPL), generates a tool path to be used in a process plan. FIG. 2 is afunctional block diagram showing a system 20 for planning supportremoval in hybrid manufacturing with the aid of a digital computer inaccordance with one embodiment. A tool path planner 21 is providedthrough a centralized server 22. The server 22 can be remotely accessedvia the Web over a wide area public data communications network, such asthe Internet, using wired or wireless connections. Users can interfacewith the server 22 through a Web browser 28 executing on a personalcomputer 27, mobile “smart” phone, or similar device. Alternatively, thetool path planner 21 can be provided locally on the personal computer 27or similar device.

The server 22 is operatively coupled to a storage device 24, withinwhich is stored models of designed parts 25 that define surfaces and theinterior of the part, such as represented using some CAD representationsuch as STEP, STL, voxels or some other solid model representation, alibrary of cutting or machining tools 26, and, in one embodiment, alibrary of motion planning algorithms, such as the Open Motion PlanningLibrary (OMPL). Both the server 22 and personal computer 27 includecomponents conventionally found in general purpose programmablecomputing devices, such as a central processing unit, memory,input/output ports, network interfaces, and non-volatile storage,although other components are possible. In addition, other computationalcomponents are possible.

In one embodiment, through the tool path planner 21, the Web-basedservice 23 generates process plans 30 that each contain support removalsequences. Each sequence includes CNC machining instructions that havebeen generated by the tool path planner 21 by modeling the inherentcapabilities of a hybrid manufacturing setup 29. The hybridmanufacturing setup 29 includes a cutting or machining tool assembly 31for performing SM operations. The machining tool assembly 29 can beprogrammed with the machining instructions in the process plans 30generated by the tool path planner 21 and operated to remove supportingbeams 12 from the near-net shape 10.

The tool path planner 21 implements a geometric engine that executes aset of spatial planning algorithms for automated manufacturabilityanalysis of arbitrary geometric models, without making assumptions onthe tool geometry and degrees of freedom, or the existence ofsurrounding tooling and fixtures, such as described in U.S. Pat. No.9,292,626, issued Mar. 22, 2016, to Nelaturi et al., the disclosure ofwhich is incorporated by reference. The manufacturing setup modelcorresponds to the library of cutting or machining tools 26 withspecifications for each operable tool, and the tool path planner 21connects the available capability of each tool to the uploaded geometricmodel of each part 25 to provide qualitatively distinct process plans,represented in the form of a JSON (“JavaScript Object Notation”) file orsimilar structured encoding or human-readable format, with detailedfeedback for each individual plan.

The geometric reasoning algorithms use tooling information from thelibrary 26 to allow the tool path planner 21 to generate acollision-free path for the tool assembly to remove one support beam 12at a time, as further described infra with reference to FIG. 3. As eachsupport beam 12 is removed, the tool path planner 21 must reason aboutaccessing the removal of the remaining support beams 12 in the contextof the space just freed up by the removal of that support beam 12. Ineach successive iteration within the support removal sequence, the toolpath planner 21 relies upon a solid model corresponding to the near-netshape 10 and all remaining support structure 12 that together constitutea physical obstacle that the machining tool assembly 31 must avoid.Thus, based upon the available space, the tool path planner 21 attemptsto find the best way to remove the next support beam 12 in the supportremoval sequence, provided that the next support beam 12 is accessibleto the machining tool assembly 31.

In modeling an SM process plan problem space, begin by assuming thatthere are finitely many (say k) support beams 12 that contact thefabricated part 11.

Each support beam 12 can be numbered and indexed, so as to generate allk! permutations of support structure removal sequences. Considering thata single part 11 being fabricated may consist of several hundred supportbeams 12, an enumeration of all k! permutations would result in anastronomically large set of possible support removal sequences.Generating and testing each possible sequence would be impracticable.

On the other hand, human engineers may be able to visually inspect anear-net shape and recommend a candidate set of support beam removalsequences based on their own experience. Importantly, a human engineermay be able to quickly decide if a near-net shape 10 has support beams12 that cannot be removed, for example, when supports support beams 12are placed in internal voids 13, and that knowledge can be used to paredown the size of the problem space. Nevertheless, relying upon humanexpertise can present shortcomings due to the limitations inherent inthe human reasoning of three-dimensional space and a fully automatedprocess plan generate and test approach for candidate sequences ofsupport removal is needed.

Algorithmic reasoning about a cutting tool assembly's space of feasibleconfigurations can be effectively harnessed by the tool path planner toconstruct a sequence of supports structures 12 that guarantees acollision-free path for the tool assembly to remove each supportstructure 12 in the sequence. FIG. 3 is a flow diagram showing a method40 for planning support removal in hybrid manufacturing with the aid ofa digital computer in accordance with one embodiment. The method 40 isperformed as a series of process or method steps performed by, forinstance, a general purpose programmed computer, such as the server 22and personal computer 27, or other programmable computing device.Initially, a model of the manufacturing setup, including a library ofthe cutting tools 26 to be used to machine the near-net shape 12, aswell as knowledge of the part 11 as designed and the scaffolding 12(available through the stored models of designed parts 25), arerespectively retrieved (steps 41 and 42). Note that initially, thenear-net shape 10 is the combination of the part 11 and the scaffolding12. The library 26 stores information on each type of milling tool,including the orientations and positions in which the milling tool canoperate. Next, for process planning purposes, the tip of the machiningtool assembly 29 is logically located (step 43) to coincide with theorigin of a coordinate system in R³. The tool assembly's tip wouldordinarily be the aspect of the machining tool 31 that makes actualphysical contact with the near-net shape 10 to remove a support beam 12from the part 11. This coordinate system is used to measure the relativepositions and orientations of the tool assembly T with respect to thenear-net shape N. Next, logically assume that there are finitely manysupport beams S={S₁, . . ., S_(k)} added on to the part P that isintended to be fabricated by the AM process (step 44). In general, kwill represent the actual number of support beams 12. Therefore, N=PU^(k) _(i=1)S_(i).

Unlike traditional machining, the entire scaffolding 12 need not becompletely machined off the near-net shape 10, though that is a feasiblestrategy. Rather, in SM processes, fracturing the region (or point) ofcontact between the support beam 12 and the part 11, so that the part 11can be disengaged from the support beam 12, will suffice. Therefore, ata minimum, collision-free contacts between the cutting tool's tip andthe region of a near-net shape 10 where a support beam 12 touches thepart's surface must be found. A greedy algorithm to plan the removal ofthe support beams 12 from the near-net shape 10 is performed (step 45),as further described infra with reference to FIG. 4 (step 46), afterwhich process plans are created (step 47) based upon the collection oftool assembly configurations that were generated and the methodcompletes.

The greedy algorithm models the motion of the tool assembly 31 throughthe free-spaces around the near-net shape 10 and the part 10 todetermine feasible points of contact for the tool assembly 31. FIG. 4 isa flow diagram showing a routine 60 for performing a greedy algorithm toplan the removal of the support beams 12 from the near-net shape 10 foruse in the method 40 of FIG. 3. First, a configuration space of rigidmotions for the tool assembly 31 (geometric transformations) is set up(step 61) by assuming that the tool assembly T can operate with all sixdegrees of freedom available for a rigid body, that is, threetranslations and three rotations. Mathematically, this assumption can beexpressed as the configuration space of rigid motions C=R³×SO(3), whereSO(3) refers to the group of 3×3 orthogonal transformations thatrepresent spatial rotations of the tool assembly T based upon the toolassembly's parameters, including orientations and positions along whichthe tool cuts away raw material. Define projections from C to R³ and toSO(3) as follows:

π₁:C→R³  (1)

π₂: C→SO(3)  (2)

Now, define the free-space

_(N) around the near-net shape N as the set of all of tool assemblyconfigurations that do not collide with the near-net shape N, that is,all non-colliding orthogonal transformations of the machining toolassembly within the configuration space C, and any workholding devices Wthat are used to fixture the part as scaffolding is removed:

_(N)={g ∈C s.t. T_(g)∩* {N ∪W}=Ø}  (3)

where the letter g emphasizing that C is also a Lie group called theSpecial

Euclidean group SE(3). Here T_(g) refers to the tool assembly Ttransformed by an element g ∈C, and ∩* refers to regularizedintersection. The complement of the free space

_(N) is called the obstacle space O that delineates configurations ofthe tool assembly T that cause collision with the near-net shape N.Therefore, the boundary shared by O and

_(N) delineates all of the tool configurations that cause contact, butno collision between the tool assembly T and the near-net shape N.

Similarly, define the free-space

_(p) around the part P as the set of all of tool assembly T'sconfigurations that do not collide with P ∪W, which is the part P andany workholding devices W.

_(p)={g ∈C s.t. T_(g)∩* {P ∪W}=Ø}  (4)

Notice that after the AM processes complete and before the SM processesstart,

_(p)⊃

_(N), that is, the free-space

_(p) around the part P is a superset of the free-space

_(N) around the near-net shape N because the support beams 12 willprevent the tool assembly T from being able to reach the physical spaceotherwise available to access the part P. As the support beams 12 areremoved, the near-net shape N will get smaller and converge in sizetowards the size of the part P, while the free-space

_(N) around the near-net shape N will get larger and converge towardsthe free-space

_(p) around the part P.

Given a boundary feature F⊂∂P, where boundary of a set Y is denoted ∂Y,two sets of collision-free contact configurations of tool assembly T atthe boundary feature F can be defined as:

_(F) ^(P)={g ∈∂F_(P)|π₁(T_(g)) ∈F}  (5)

_(F) ^(N)={g ∈∂F_(N) |π₁(T_(g)) ∈F}  (6)

The intersection of each support beam S_(i) ∈ S with the part P will bea boundary feature F_(i). For simplicity, assume that boundary featureF_(i) is a point set, which is consistent with AM practice, wheresupport beams S are often designed to have minimal contact with theboundary of the part ∂P to minimize surface roughness and enable easierfracture and removal of the support beams S by SM processes.

Next, the manner of construction of the support beams 12 is determined(step 62) to provide boundary features at the intersection of theindividual support beam S_(i) and the part P. Preferably, support beamsare constructed from a surface of ∂P to a stationary base plate orfixture. However, in some situations, the support beams 12 may have tobe constructed from one location of ∂P to another location of ∂P. Also,an individual support beam S_(i) may contact the part P at multiplelocations when the contacting support beams are “branched” outwards froma main “trunk,” such as occurs when the scaffolding is organized intree-like shapes. To accommodate these situations, a specific boundaryfeature F_(i)=S_(i)∩ P can be a discrete point set, which is theintersection of the individual support beam S_(i) and the part P.Therefore, if

^(N) _(F) _(i) ≠ Ø, where

R^(N) _(F) _(i) is the set of collision-free contact configurations oftool assembly T at the boundary feature F_(i), then each ƒ ∈ F_(i) suchthat π₁(

^(N) _(F) _(i) )=ƒ, is a feasible point of contact for the tool assemblyT within the configuration space C to either partially or totally removethe individual support beam S_(i).

The part 11 is then evaluated for manufacturability (step 63), asfurther described infra with reference to FIG. 5. If a part beingfabricated 11 is non-manufacturable (step 64), no SM process plan to cutthe support beams S from the near-net shape N so that the part P can bedislodged, exists and the greedy algorithm terminates.

On the other hand, if a part being fabricated 11 is manufacturable (step64), that is, boundary features F_(i) have been found for all of thesupport beams S, a collection of tool assembly configurations that areguaranteed to be non-colliding but which can access all points in theboundary features F_(i) can be generated (step 65) using the supportremoval sequence, after which the greedy algorithm terminates. In afurther embodiment, human engineers can validate the process plans and,if desired, re-order the support removal sequence. The reordered supportremoval sequence is resubmitted to the greedy algorithm to attempt tore-plan the tool motions to remove the supports without collision,starting with determining the manner of construction of the supportbeams 12 (step 62) based upon the reordered support removal sequence.

Hybrid manufacturability hinges upon the ability to remove the supportbeams 12 from a near-net shape 10 to yield the part 11. FIG. 5 is a flowdiagram showing a recursive routine 80 for evaluating manufacturabilityof a part being fabricated 11 for use in the routine 60 of FIG. 4. Theroutine is recursive, although an iterative structure could be usedinstead. Assuming that there are still support beams S_(i) remaining inthe set of support beams S (step 81), all of those support beams S_(i)are evaluated to find an individual support beam S_(i) where π₁(

^(N) _(F) _(i) )=F_(i)(step 82), that is, F_(i) is a feature along theboundary of the near-net shape 10 that constitutes a feasible point ofcontact for the tool assembly T to either partially or totally removethe individual support beam S_(i). If an individual support beam S_(i)does not exist (step 83), the part P is found to be non-manufacturable(step 84) because no SM process plan to cut the support beams S from thenear-net shape N, so that the part P can be dislodged exists. However,if such an individual support beam S_(i) does exist (step 83), then byconstructing

^(N) _(F) _(i) , which is the set of collision-free contactconfigurations of tool assembly Tat the boundary feature F_(i), acollection of tool assembly configurations that are guaranteed to benon-colliding but which can access all points in F_(i) can be extracted.The near-net shape 10 is continually updated as each support beam S_(i)is incrementally removed. Thus, the near-net shape N is updated tobecome N-S_(i) (step 85), the individual support beam S_(i) is removedfrom the set of remaining support beams S (step 86), and individualsupport beam S_(i) is added to the support removal sequence (step 87).The routine recurses (or iterates) until no support beams S remain inthe set (step 81), or the part P is found to be non-manufacturable (step84) for a given sequence of support beams to be removed.

There may be multiple individual support beams S_(i) that are eligiblefor removal at each recursion (or iteration), that is, multiple supportbeams S_(i) may satisfy the condition that π₁(

^(N) _(F) _(i) )=F_(i) (step 82). The choice of a particular individualsupport beam S_(i) then affects how the near-net shape N is updated,which in turn affects the subsequent collision-free contactconfigurations

^(N) _(F) of tool assembly T at the boundary feature F. A tool pathplanner 21 that uses motion planning algorithms, for instance, the OMPL,cited supra, may be used to choose a particular support beam 12 and planthe individual tool assembly trajectories from the chosen support beam12 to the next support beam 12 in the support removal sequence. Thechallenge with this approach, though, is computing the collision-freecontact configurations

^(N) _(F) _(i) of tool assembly T at the boundary feature F_(i) at eachiteration of the support removal sequence, as the near-net shape N isupdated as each support beam 12 is removed, which occurs in thesix-dimensional configuration space C, as discussed in detail infra.Furthermore, limited accessibility may require complex tool paths toexecute (if possible). Nevertheless, the greedy algorithm will alwaysreturn a valid sequence of support removals if such a sequence exists.

In practical situations, several collision-free support removalsequences may be possible and various combinations of collision-freecontact configurations

^(N) _(F) _(i) may need to be explored to find optimal removalsequences. A “good” sequence could be determined by evaluating thecandidate process plans based upon a manufacturing heuristic,optimization constraint, or cost constraint sought to be optimized, forinstance, minimizing time, using as few orientations as possible forthree-axis milling, or maximizing surface finish, such as described inU.S. Patent application Pub. No. US 2017/0220028, filed Jan. 29, 2016,pending, the disclosure of which is incorporated by reference. One ormore qualitatively distinct process plans for machining a part throughSM processes are created; the surfaces of the part are modeled andparameters for a plurality of cutting tools are obtained. The parametersinclude orientations and positions along which each cutting tool cutsaway raw material. Each process plan includes a maximal set oftranslations for each cutting tool, where each translation includes acollision-free orientation of the cutting tool and a maximal machinablevolume of material removable from the part in that orientation. A searchengine navigates through a hierarchically-structured search space thatstarts at an initial state and transitions to successive states based onactions that satisfy a cost constraint function. One of the actions ischosen as guided by a heuristic that is based on aggregate cost and thenegative volume that remains after subtracting the maximal sub-volumefor the action chosen. Each state and each action includes a tool,orientation of the tool, and a maximal machinable volume. The searchends when a goal condition is satisfied and the actions that satisfy thecost constraint function constitute the process plan to be used.

More generally, to optimize the sequencing of SM processes, a searchspace can be iteratively built where each search node stores distinctboundary features F_(N) for the near-net shape N as obtained bycalculating the free-space

_(N) around the near-net shape N resulting from subtracting a distinctsupport beam S_(i) ∈ S from the near-net shape N. Several practicalheuristics may be used to pick the support beams 12 that are goodcandidates for removal. For example, visibility analysis formanufacturing algorithms may be used to decide which of the F_(i) havethe most visibility because visibility can be used as a weak conditionfor accessibility. Furthermore, there may be practical considerationsabout how much deviation from the surface normal can be allowed for thetool contact orientations to minimize scalloping the part surface.Therefore, a limited set of cutting tool assembly orientations may bechosen a priori to minimize the number of cutting tool assemblyorientations for which the free-spaces need to be computed.

The six-dimensional configuration space of obstacles and free-space forcomplex cutting tool and fixture assemblies can be effectively modeledto compute the collision-free contact configurations

^(N) _(F) _(i) of tool assembly T at the boundary feature F_(i) at eachiteration of a support removal sequence, such as described in S.Nelaturi, Configuration Modeling, Ph.D. Dissertation, Univ. ofWisconsin-Madison (2012), and U.S. Pat. No. 9,235,658, issued Jan. 12,2016, to Nelaturi et al., and U.S. Pat. No. 9,566,697, issued Feb. 14,2017, to Nelaturi et al., the disclosures of which are incorporated byreference. Given a collection of orientations sampled to a desireddensity, the six-dimensional spaces can be computed by calculating thethree-dimensional translational free-space for each sampled orientation.In practice, computing the obstacle space, that is, the complement ofthe free-space, may be more convenient to compute since the obstaclespace is a closed and bounded set. By computing the six-dimensionalobstacle space, all of the contact configurations at a specific locationcan be retrieved by querying the boundary of the six-dimensionalobstacle in time linear to the number of sampled orientations. Thecollision-free contact configurations

^(N) _(F) _(i) can be obtained by querying the contact configurations ateach F_(i).

More generally, given a collection of free-spaces obtained byiteratively reducing the number of support beams, standard searchalgorithms, such as A* (with an implemented cost function), can be usedto find the best sequence of free-spaces that will provide a low-leveltool path planner that uses motion planning algorithms, for instance,the OMPL, cited supra, all the available configurations to find a toolpath from one support beam to the next support beam, and execute thesupport removal.

While the invention has been particularly shown and described asreferenced to the embodiments thereof, those skilled in the art willunderstand that the foregoing and other changes in form and detail maybe made therein without departing from the spirit and scope of theinvention.

What is claimed is:
 1. A system for planning support removal in hybrid manufacturing with the aid of a digital computer, comprising the steps of: a computer, comprising: a storage device, comprising: parameters for a machining tool assembly, each parameter comprising orientations and positions of the machining tool assembly; a model of a part defining surfaces and the interior of the part and one or more support structures that were added to the part during additive manufacturing; and a near-net shape initially modeled as the part combined with the support structures; and a processor and memory within which code for execution by the processor is stored to perform the steps comprising: setting up a configuration space comprising geometric transformations that represent the spatial motions of the machining tool assembly based upon the machining tool assembly's parameters; determining a manner of construction of each of the support structures to provide contact features at an intersection of the support structures and the part; evaluating each of the support structures for the existence of a contact feature within free-space that is available within the configuration space around the near-net shape that comprises a feasible region of contact for the tool assembly to remove all of the support structures that are accessible from the near-net shape, wherein the support structure is added to a support removal sequence and the near-net shape is continually updated as each support structure is incrementally removed; constructing for each of the support structures in the support removal sequence a set of collision-free contact configurations of the machining tool assembly at the contact feature, provided that contact features are found for all of the support structures; creating process plans comprising machining operations by the machining tool assembly based upon the sets of collision-free contact configurations of the machining tool assembly for the support structures; and programming the machining tool assembly with the process plans and operating the machining tool assembly per the machining operations in the process plans by machining off the support structures.
 2. A system in accordance with claim 1, further comprising code for execution by the processor to perform the steps comprising: defining the free-space around the near-net shape as the set of all of the machining tool assembly geometric transformations of the machining tool assembly that do not collide with the near-net shape and any workholding devices that are used to fixture the part as the support structures are removed.
 3. A system in accordance with claim 2, wherein the free-space around the near-net shape N is defined in accordance with:

_(N)={g ∈ C s.t. T_(g)∩* {N ∪W}=Ø} where C represents the configuration space, T_(g) refers to the machining tool assembly transformed by an element g ∈ C, ∩* refers to regularized intersection, and W represents any workholding devices.
 4. A system in accordance with claim 3, wherein each ƒ∈ F_(i), where ƒ is a feasible region of contact for the tool assembly T within the configuration space C to either partially or totally remove the individual support beam S_(i), is defined in accordance with: π₁(

^(N) _(F) _(i) )=ƒ where

^(N) _(F) _(i) is the set of collision-free contact configurations of tool assembly T at the contact feature F_(i), provided that

^(N) _(F) _(i) ≠Ø.
 5. A system in accordance with claim 4, wherein F_(i) comprises a discrete point set comprising the intersection i of the support beam S_(i) being evaluated and the part P.
 6. A system in accordance with claim 1, further comprising code for execution by the processor to perform the steps comprising: modeling the near-net shape with the computer as the part combined with the support structures minus the support structure being evaluated; and removing with the computer the support structure being evaluated from the model of the support structures.
 7. A system in accordance with claim 1, further comprising code for execution by the processor to perform the steps comprising: finding with the computer that the part is non-manufacturable when no contact feature within free-space around the near-net shape that comprises a feasible region of contact for the tool assembly within the configuration space to remove the support structure from the near-net shape exists.
 8. A system in accordance with claim 1, further comprising code for execution by the processor to perform the steps comprising: generating with the computer a plurality of support removal sequences; and selecting with the computer one of the support removal sequences based upon an optimization constraint.
 9. A system in accordance with claim 8, further comprising code for execution by the processor to perform the steps comprising: representing in the computer a set of states, each state identifying one of the orientations of the machining tool assembly and describing a negative volume of the part, with one of the states representing an initial state; representing with the computer a set of actions, each action one of the orientations of the machining tool assembly and describing the maximal sub-volume of material removable from the negative volume of the part by the machining tool assembly; and repetitively transitioning with the computer, starting at the initial state, from one of the states to another of the states by choosing one of the actions as guided by a heuristic that is based on aggregate cost and the negative volume that remains after subtracting the maximal sub-volume for the action chosen.
 10. A system in accordance with claim 1, further comprising code for execution by the processor to perform the step comprising: choosing one of the support structures with the computer for evaluating the support structure for the existence of a contact feature through a motion planning algorithm.
 11. A system in accordance with claim 1, further comprising code for execution by the processor to perform the step comprising: reordering the support removal sequence and re-attempting to create the process plans beginning with the step of determining with the computer a manner of construction of each of the support structures based upon the reordered support removal sequence.
 12. A method for planning support removal in hybrid manufacturing with the aid of a digital computer, comprising the steps of: providing a computer with parameters for a machining tool assembly, each parameter comprising orientations and positions of the machining tool assembly; providing the computer with a model of a part defining surfaces and the interior of the part and one or more support structures that were added to the part during additive manufacturing and modeling a near-net shape with the computer initially as the part combined with the support structures; setting up with the computer a configuration space comprising geometric transformations that represent the spatial motions of the machining tool assembly based upon the machining tool assembly's parameters; determining with the computer a manner of construction of each of the support structures to provide contact features at an intersection of the support structures and the part; evaluating each of the support structures with the computer for the existence of a contact feature within free-space that is available within the configuration space around the near-net shape that comprises a feasible region of contact for the tool assembly to remove all of the support structures that are accessible from the near-net shape, wherein the support structure is added to a support removal sequence and the near-net shape is continually updated as each support structure is incrementally removed; constructing with the computer for each of the support structures in the support removal sequence a set of collision-free contact configurations of the machining tool assembly at the contact feature, provided that contact features are found for all of the support structures; creating process plans comprising machining operations by the machining tool assembly with the computer based upon the sets of collision-free contact configurations of the machining tool assembly for the support structures; and programming the machining tool assembly with the computer with the process plans and operating the machining tool assembly per the machining operations in the process plans by machining off the support structures.
 13. A method in accordance with claim 12, further comprising the step of: defining the free-space around the near-net shape with the computer as the set of all of the machining tool assembly geometric transformations of the machining tool assembly that do not collide with the near-net shape and any workholding devices that are used to fixture the part as the support structures are removed.
 14. A method in accordance with claim 13, wherein the free-space

_(N) around the near-net shape Nis defined in accordance with:

_(N)={g ∈ C s.t. T_(g)∩* {N ∪ W}=Ø} where C represents the configuration space, T_(g) refers to the machining tool assembly transformed by an element g ∈ C, ∩* refers to regularized intersection, and W represents any workholding devices.
 15. A method in accordance with claim 14, wherein each ƒ∈F_(i), where ƒ is a feasible region of contact for the tool assembly T within the configuration space C to either partially or totally remove the individual support beam S_(i), is defined in accordance with: π₁(

^(N) _(F) _(i) )=ƒ where

^(N) _(F) _(i) is the set of collision-free contact configurations of tool assembly T at the contact feature F_(i), provided that

^(N) _(F) _(i) ≠Ø.
 16. A method in accordance with claim 15, wherein F_(i) comprises a discrete point set comprising the intersection i of the support beam S_(i) being evaluated and the part P.
 17. A method in accordance with claim 12, wherein the near-net shape is continually updated comprising the steps of: modeling the near-net shape with the computer as the part combined with the support structures minus the support structure being evaluated; and removing with the computer the support structure being evaluated from the model of the support structures.
 18. A method in accordance with claim 12, further comprising the step of: finding with the computer that the part is non-manufacturable when no contact feature within free-space around the near-net shape that comprises a feasible region of contact for the tool assembly within the configuration space to remove the support structure from the near-net shape exists.
 19. A method in accordance with claim 12, further comprising the steps of: generating with the computer a plurality of support removal sequences; and selecting with the computer one of the support removal sequences based upon an optimization constraint.
 20. A method in accordance with claim 19, further comprising the steps of: representing in the computer a set of states, each state identifying one of the orientations of the machining tool assembly and describing a negative volume of the part, with one of the states representing an initial state; representing with the computer a set of actions, each action one of the orientations of the machining tool assembly and describing the maximal sub-volume of material removable from the negative volume of the part by the machining tool assembly; and repetitively transitioning with the computer, starting at the initial state, from one of the states to another of the states by choosing one of the actions as guided by a heuristic that is based on aggregate cost and the negative volume that remains after subtracting the maximal sub-volume for the action chosen.
 21. A method in accordance with claim 12, further comprising the step of: choosing one of the support structures with the computer for evaluating the support structure for the existence of a contact feature through a motion planning algorithm.
 22. A method in accordance with claim 12, further comprising the step of: reordering the support removal sequence and re-attempting to create the process plans beginning with the step of determining with the computer a manner of construction of each of the support structures based upon the reordered support removal sequence. 